Question

Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm.

Answer 1

Radius of first circle = r₁ = 15 cm

Radius of second circle = r₂ = 18 cm

∴ Circumference of first circle = 2πr₁ = 30π cm

Circumference of second circle = 2πr₂ = 36π cm

Let the radius of the circle = R

According to the question,

Circumference of circle = Circumference of first circle + Circumference of second circle

2πR = 2πr₁ + 2πr₂

⇒ 2πR = 30π + 36π

⇒ 66π 

⇒ R = 33

⇒ Radius = 33 cm

Hence, required radius of a circle is 33 cm.